Recently, photonic crystals are becoming increasingly important as devices for controlling electromagnetic waves such as light. A photonic crystal is a periodical structured member showing a periodical change in a dielectric constant in crystal-constituting regions, with a periodical dielectric change comparable to a wavelength of an electromagnetic wave such as light, and can realize novel electromagnetic characteristics by an artificial periodical structure. Such structure is featured, like a band gap formation in a semiconductor substance by a Bragg reflection of electrons by periodical potentials of atomic nuclei, by a formation of band gap to an electromagnetic wave such as light, as such electromagnetic wave is subjected to a Bragg reflection by periodical distribution of refractive index. In a photonic crystal, such band gap is called a photonic band gap. Such photonic band gap, in which an electromagnetic wave such as light cannot exist, allows to arbitrarily control the electromagnetic wave such as light.
A band gap which inhibits a propagation of an electromagnetic wave such as light in all the directions is called a complete band gap. In case such complete band gap is made possible, an ultra small device can be prepared in a photonic crystal, by forming a point defect or a linear defect therein. For example, in case of artificially perturbing a part of a periodicity in the photonic crystal, a defect level is formed in the photonic band gap and an electromagnetic wave such as light is allowed to exist only in such defect level, and such phenomenon can be utilized for example in a resonator. Also in case of forming a linear defect, an electromagnetic wave such as light can propagate along an array of defects but cannot propagate in other areas than the defects, so that an ultra small waveguide can be formed.
Therefore, in order to exploit the characteristics of the photonic band gap, it is necessary to prepare a photonic crystal having a complete band gap.
As a photonic crystal structure having a wide complete band gap, there is known a photonic crystal having a three-dimensional periodical structure (hereinafter represented as three-dimensional photonic crystal) such as a Yablonovite structure (for example Patent Literature 1) or a Woodpile structure (for example Non-Patent Literature 1). Such crystals have a wide complete band gap, but are very difficult to produce because of structures thereof Also in case one of the plural dielectric substances constituting the photonic crystal is air, the three-dimensional periodical structure cannot be maintained when the dielectric substances are arranged three-dimensionally and in a non-contact manner as in a certain diamond or opal structure.
On the other hand, a photonic crystal having a two-dimensional periodical structure (hereinafter represented as two-dimensional photonic crystal) is easier to prepare in comparison with the three-dimensional photonic crystal. For example, as a two-dimensional photonic crystal having a complete band gap, there is known a two-dimensional photonic crystal constituted of a triangular lattice arrangement formed by a circular hole (for example Patent Literature 2). Also as a relatively easily produceable structure, a two-dimensional photonic crystal having a tetragonal lattice arrangement formed by circular holes or cylinders is known.
Also the photonic crystal is formed from two or more dielectric substances. Ordinarily there are employed two substances, one of which is often air because of an ease in manufacture and a low loss. For example, in the aforementioned two-dimensional photonic crystal constituted of a trigonal lattice structure or a tetragonal lattice structure, such trigonal lattice or tetragonal lattice is formed by air.
Patent Literature 1: U.S. Pat. No. 5,172,267
Patent Literature 2: JPA No. 2001-272555 (paragraph [0023], FIG. 1)
Non-Patent Literature 1: E. Knobloch, A. Deane, J. Toomre and D. R. Moore, Contemp. Math., 56, 203 (1986).
However, in the two-dimensional photonic crystal constituted of a trigonal lattice arrangement as described in Patent Literature 2, a widest complete band gap is obtained for r/a of 0.48 (wherein r is a radius of a circular hole and a is a lattice constant of the photonic crystal). Therefore, a thickness between the circular holes becomes as small as 0.04a, and such photonic crystal is very difficult to prepare.
Also a two-dimensional photonic crystal constituted of a tetragonal lattice structure, in case the tetragonal lattice is formed by circular holes, shows a band gap to a TE wave (transverse electric wave) of the incident electromagnetic wave but does not show a band gap to a TM wave (transverse magnetic wave). On the other hand, in case the tetragonal lattice is formed by cylinders, it shows a band gap to the TM wave but does not show a band gap to the TE wave. Therefore, a complete band gap cannot be obtained in the two-dimensional photonic crystals constituted by such tetragonal lattices.
Thus, there is required a two-dimensional photonic crystal that can be prepared easily and that shows band gaps to both the TE wave and the TM wave in all the incident angles in order to obtain a complete band gap.
On the other hand, as the photonic crystal is generally prepared by a semiconductor manufacturing technology and a photoforming technology, materials to be employed are limited to semiconductor materials and photosettable resins. These materials have relatively small relative dielectric constants, so that a wide band gap is difficult to obtain. A method of mixing a ceramic powder in a photosettable resin is also known, but a high relative dielectric constant cannot be obtained as the relative dielectric constant is governed by a logarithmic mixing rule and is principally influenced by the relative dielectric constant of the resin, so that a wide band gap is difficult to obtain.